We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The considered multiplier functions are finitely smooth and satisfy an integral condition at infinity. In particular multipliers of compact support are admitted.

Wrobel, B. (2015). On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates [Altro].

On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates

WROBEL, BLAZEJ JAN
Primo
2015

Abstract

We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The considered multiplier functions are finitely smooth and satisfy an integral condition at infinity. In particular multipliers of compact support are admitted.
Altro
Scientifica
Mathematics - Functional Analysis; Mathematics - Functional Analysis; 47A60, 42B25, 42B15
English
2015
Wrobel, B. (2015). On the consequences of a Mihlin-Hörmander functional calculus: maximal and square function estimates [Altro].
Wrobel, B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/85763
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